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In Exercises 13–20, find the particular solution corresponding to the tableau.
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Chapter 4 Solutions
Finite Mathematics & Its Applications (12th Edition)
- Q. Table provided gives data on gross domestic product (GDP) for the United States for the years 1959–2005. a. Plot the GDP data in current and constant (i.e., 2000) dollars against time. b. Letting Y denote GDP and X time (measured chronologically starting with 1 for 1959, 2 for 1960, through 47 for 2005), see if the following model fits the GDP data: Yt = β1 + β2 Xt + ut Estimate this model for both current and constant-dollar GDP. c. How would you interpret β2? d. If there is a difference between β2 estimated for current-dollar GDP and that estimated for constant-dollar GDP, what explains the difference? e. From your results what can you say about the nature of inflation in the United States over the sample period?arrow_forwardEXAMPLE 6.56 If λ = 2 per hour and u = 4 per hour in a 2-capacity single- server queueing system, find the effective arrival rate.arrow_forward(3) Show that for a, b E R we have |a+b| + |ab| = 2 max{|a|, |b|}.arrow_forward
- In Exercises 13–17, determine conditions on the bi ’s, if any, in order to guarantee that the linear system is consistent. 13. x1 +3x2 =b1 −2x1 + x2 =b2 15. x1 −2x2 +5x3 =b1 4x1 −5x2 +8x3 =b2 −3x1 +3x2 −3x3 =b3 14. 6x1 −4x2 =b1 3x1 −2x2 =b2 16. x1 −2x2 − x3 =b1 −4x1 +5x2 +2x3 =b2 −4x1 +7x2 +4x3 =b3 17. x1 − x2 +3x3 +2x4 =b1 −2x1 + x2 + 5x3 + x4 = b2 −3x1 +2x2 +2x3 − x4 =b3 4x1 −3x2 + x3 +3x4 =b4arrow_forwardCould you solve (A) with the set A? Thank you.arrow_forwardConsider the set S = {4x + 1, 2x 8, 4x + a}. The set S spans P2. %3D If t(x) = 8x - 9a +43 e P2, then t can be written as a linear combination of elements of S. That is, t(x) : (4a + 1) + b. (2a – 8) + c (-4x2 + a). = a. Determine a, b, and c a = b. C = %3Darrow_forward
- National Debt The size of the total debt owed by the UnitedStates federal government continues to grow. In fact,according to the Department of the Treasury, the debt perperson living in the United States is approximately $53,000(or over $140,000 per U.S. household). The following datarepresent the U.S. debt for the years 2001–2014. Since thedebt D depends on the year y, and each input correspondsto exactly one output, the debt is a function of the year. SoD1y2 represents the debt for each year y. Source: www.treasurydirect.govDebt (billions Debt (billionsYear of dollars) Year of dollars)2001 5807 2008 10,0252002 6228 2009 11,9102003 6783 2010 13,5622004 7379 2011 14,7902005 7933 2012 16,0662006 8507 2013 16,7382007 9008 2014 17,824 (a) Plot the points 12001, 58072, 12002, 62282, and so on ina Cartesian plane.(b) Draw a line segment from the point 12001, 58072 to12006, 85072. What does the slope of this line segmentrepresent?(c) Find the average rate of change of the debt from 2002…arrow_forwardSolve the determinearrow_forwardcan u solve g,h,iarrow_forward
- The table below gives adult wine consumption.arrow_forwardSection 2.2 2.1. Solve the following difference equations: (a) Yk+1+Yk = 2+ k, (b) Yk+1 – 2Yk k3, (c) Yk+1 – 3 (d) Yk+1 – Yk = 1/k(k+ 1), (e) Yk+1+ Yk = 1/k(k+ 1), (f) (k + 2)yk+1 – (k+1)yk = 5+ 2* – k2, (g) Yk+1+ Yk = k +2 · 3k, (h) Yk+1 Yk 0, Yk = ke*, (i) Yk+1 Bak? Yk (j) Yk+1 ayk = cos(bk), (k) Yk+1 + Yk = (-1)k, (1) - * = k. Yk+1 k+1arrow_forwardDoes moderate alcohol consumption impact the performance of heavy machinery opera- tors in the workplace? A large stevedoring company studied the time on task (in seconds) to complete a complex manoeuvre by crane operators on the dock, firstly in a completely sober condition, and then five days later, after consuming a moderate amount of alcohol (as measured by a blood alcohol test). The data are given below: Operator Time taken while sober| Time taken after consuming alcohol 1 2 دانه 3 4 5 6 7 8 9 10 186 375 310 240 220 420 410 205 250 900 262 565 800 630 285 365 405 735 425 900 (a) Does moderate alcohol consumption increase the time it takes to complete a complex crane manoevure on the docks? Use an appropriate non-parametric test at a = 0.05 to support your conclusion. (b) Give a normal approximation to the above test (ignore that n is less than 25). Comment on the outcomes of the two different tests at the 1% level of significance.arrow_forward
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage